Ubiquity of density slope oscillations in the central regions of galaxy and cluster-sized systems

One usually thinks of a radial density profile as having a monotonically changing logarithmic slope, such as in NFW or Einasto profiles. However, in two different classes of commonly used systems, this is often not the case. These classes exhibit non-monotonic changes in their density profile slopes which we call oscillations for short. We analyze these two unrelated classes separately. Class 1 consists of systems that have density oscillations and that are defined through their distribution function f(E), or differential energy distribution N(E), such as isothermal spheres, King profiles, or DARKexp, a theoretically derived model for relaxed collisionless systems. Systems defined through f(E) or N(E) generally have density slope oscillations. Class 1 system oscillations can be found at small, intermediate, or large radii but we focus on a limited set of Class 1 systems that have oscillations in the central regions, usually at log(r/r_-2) ∼ -2, where r_-2 is the largest radius where dlog(ρ)/dlog(r) = -2. We show that the shape of their N(E) can roughly predict the amplitude of oscillations. Class 2 systems which are a product of dynamical evolution, consist of observed and simulated galaxies and clusters, and pure dark matter halos. Oscillations in the density profile slope seem pervasive in the central regions of Class 2 systems. We argue that in these systems, slope oscillations are an indication that a system is not fully relaxed. We show that these oscillations can be reproduced by small modifications to N(E) of DARKexp. These affect a small fraction of systems' mass and are confined to log(r/r_-2) ∼ 0. The size of these modifications serves as a potential diagnostic for quantifying how far a system is from being relaxed.